MATH231 Practice Exam 1

# MATH231 Practice Exam 1 - Math 231 Practice Exam 2...

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Math 231 Practice Exam 2 Instructions: This is a practice exam. Please treat it as a regular exam: sit down and take it in 50 minutes without interruption and without reference to the textbook or to the class notes.When answering questions on the convergence or divergence of a sequence or series you MUST give a proof or cite an appropriate theorem or theorems. 1

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Problem 1: State as brieﬂy and concisely as you can the following theorems/tests. List all hypothesis and the conclusions. Your statement should be formulated “If (hypothesis) Then (conclusions).” If it is possible for the test to fail so indicate. (i) Integral Test (ii) Limit Comparison Test (iii) Comparison Test for SEQUENCES (iv) k th Term Test 2
Problem 2: Short Answer: (i) A sequence is decreasing ( a n +1 < a n ) and bounded above ( a n < 1 for all n ). Is it necessarily true that the sequence converges? Either show that the sequence must converge or give an example which does not converge. (ii) A sequence is increasing (

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## This test prep was uploaded on 04/07/2008 for the course MATH 231 taught by Professor Bronski during the Spring '08 term at University of Illinois at Urbana–Champaign.

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MATH231 Practice Exam 1 - Math 231 Practice Exam 2...

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